notes over 11.4 infinite geometric sequences the sum of an infinite geometric series is: provided l...
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Notes Over 11.4Infinite Geometric SequencesInfinite Geometric Sequences
The sum of an infinite geometric series is:
r
aS
11
provided l r l < 1.
If l r l > 1, then the series has no sum.
r
aS
11
3
0 2
13 .1
n
n
Notes Over 11.4Infinite Geometric SequencesInfinite Geometric Sequences
Find the sum of the infinite geometric series, if it has one.
2
1 3
0
1
a 3
2
1
213
6
r
aS
11
2
0 2
12 .2
n
n
Notes Over 11.4Infinite Geometric SequencesInfinite Geometric Sequences
Find the sum of the infinite geometric series, if it has one.
2
1 2
0
1
a 2
2
1
3
4
232
r
aS
11
1
1
19.0 .3n
n
Notes Over 11.4Infinite Geometric SequencesInfinite Geometric Sequences
Find the sum of the infinite geometric series, if it has one.
9.0 01 a 1 9.0
101.0
1
sum. no has series the,13
4 since
0 3
43 .4
n
n
Notes Over 11.4Infinite Geometric SequencesInfinite Geometric Sequences
Find the sum of the infinite geometric series, if it has one.
r
aS
11
9 ,30 .5 1 aS
Notes Over 11.4Infinite Geometric SequencesInfinite Geometric Sequences
Find the common ratio of the infinite series with the given sum and first term.
30 9
r3030 30
21r9
2130 r 10
7
r
aS
11
4 ,3 .6 1 aS
Notes Over 11.4Infinite Geometric SequencesInfinite Geometric Sequences
Find the common ratio of the infinite series with the given sum and first term.
3 4
r33
3
1r
413 r
r
aS
11
1 ,2 .7 1 aS
Notes Over 11.4Infinite Geometric SequencesInfinite Geometric Sequences
Find the common ratio of the infinite series with the given sum and first term.
2 1
r22
2
1r
112 r
r
aS
11
20 ,100 .8 1 aS
Notes Over 11.4Infinite Geometric SequencesInfinite Geometric Sequences
Find the common ratio of the infinite series with the given sum and first term.
100 20
r100100 100
80r
2080100 r 5
4
32 1.11.11.1
r
aS
11
111.0 .9
Notes Over 11.4Infinite Geometric SequencesInfinite Geometric Sequences
Write the repeating decimal as a fraction.
1.1.
9.
1.
9
1
32 1.31.31.3
r
aS
11
333.0 .10
Notes Over 11.4Infinite Geometric SequencesInfinite Geometric Sequences
Write the repeating decimal as a fraction.
1.3.
9.
3.
9
3
3
1
201.7101.71
r
aS
11
7171.0 .11
Notes Over 11.4Infinite Geometric SequencesInfinite Geometric Sequences
Write the repeating decimal as a fraction.
01.71.
99.
71.
99
71
201.2701.27
r
aS
11
2727.0 .12
Notes Over 11.4Infinite Geometric SequencesInfinite Geometric Sequences
Write the repeating decimal as a fraction.
01.27.
99.
27.
99
27
11
3
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